We solved the problem of the dielectric sphere in a uniform field.

Many questions came up, about boundaries, about Legendre Polynomials, and especially about the physical meaning of the various approximations used in the calculation.

We also went over the concept of dipole moment, and we compared the solution for the dielectric sphere by singling out the dipole contribution with a characteristic 1/r² behavior of the potential, to the classical dipole configuration with two pointlike charges.

Next classes will be on multipoles.

We are on Ch. 4 of Jackson.

1) A long cylindrical rod is placed in a uniform field E. The rod has radius "a" and dielectric constant epsilon. The rod lies perpendicular to the electric field. Find the potential inside and outside the rod

2) A dipole p= 3 j + 4 k (C m) is placed at the origin of a system of axes in an electric field of initial value E= 12 i + (4+z) j (N/C). Find the torque, the potential energy and the force on the dipole.

3) A circular disk of radius R has a uniform surface charge density, sigma. Find the electric field on the axis of the disk, at a distance z from the disk.

4) By direct integration, find the electric field at the center of a cylinder of radius R and height L, oriented along the z-axis and having a charge density rho(z)=constant + b z.
(Hint: the origin is a the center of the cylinder). Due by the end of the week!